1 Protein Classification with Improved Topological 2 Data Analysis 3 Tamal Dey 4 Department of Computer Science and Engineering, The Ohio State University, Columbus, USA 5 [email protected] 6 http://web.cse.ohio-state.edu/~dey.8/ 7 Sayan Mandal 8 Department of Computer Science and Engineering, The Ohio State University, Columbus, USA 9 [email protected] 10 http://web.cse.ohio-state.edu/~mandal.25/ 11 Abstract 12 Automated annotation and analysis of protein molecules have long been a topic of interest due to 13 immediate applications in medicine and drug design. In this work, we propose a topology based, 14 fast, scalable, and parameter-free technique to generate protein signatures. 15 We build an initial simplicial complex using information about the protein’s constituent atoms, 16 including its radius and existing chemical bonds, to model the hierarchical structure of the mo- 17 lecule. Simplicial collapse is used to construct a filtration which we use to compute persistent 18 homology. This information constitutes our signature for the protein. In addition, we demon- 19 strate that this technique scales well to large proteins. Our method shows sizable time and 20 memory improvements compared to other topology based approaches. We use the signature to 21 train a protein domain classifier. Finally, we compare this classifier against models built from 22 state-of-the-art structure-based protein signatures on standard datasets to achieve a substantial 23 improvement in accuracy. 24 2012 ACM Subject Classification Applied Computing → Life and medical sciences 25 Keywords and phrases topological data analysis, persistent homology, simplicial collapse, super- 26 vised learning, topology based protein feature vector, protein classification 27 Digital Object Identifier 10.4230/LIPIcs.WABI.2018.6 28 Supplement Material http://web.cse.ohio-state.edu/~dey.8/proteinTDA 29 Acknowledgements This work has been supported by NSF grants CCF-1318595, CCF-1526513, 30 and CCF-1733798. 31 1 Introduction 32 Proteins are by far the most anatomically intricate and functionally sophisticated molecules 33 known. The benchmarking and classification of unannotated proteins have been done by 34 researchers for quite a long time. This effort has direct influence in understanding behavior of 35 unknown proteins or in more advanced tasks as genome sequencing. Since the sheer volume 36 of protein structures is huge, up till the last decade, it had been a cumbersome task for 37 scientists to manually evaluate and classify them. For the last decade, several works aiming 38 at automating the classification of proteins have been developed. The majority of annotation 39 and classification techniques are based on sequence comparisons (for example in BLAST [19], 40 HHblits [2] and [18]) that try to align protein sequences to find homologs or a common 41 ancestor. However, since those methods focus on finding sequence similarity, they are more © Tamal K. Dey and Sayan Mandal; licensed under Creative Commons License CC-BY 18th International Workshop on Algorithms in Bioinformatics (WABI 2018). Editors: Laxmi Parida and Esko Ukkonen; Article No. 6; pp. 6:1–6:13 Leibniz International Proceedings in Informatics Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany 6:2 Protein Classification with Improved Topological Data Analysis 42 efficient in finding close homologs. Some domains such as remote homologs are known to 43 have less than 25% sequential similarity and yet have common ancestors and are functionally 44 similar. So, we miss out important information on structural variability while classifying 45 proteins solely based on sequences. Even though, sometimes, homology is established by 46 comparing structural alignment [14], accurate and fast structural classification techniques for the rapidly expanding Protein Data Bank remains a challenge. Figure 1 Workflow of our technique 47 48 Several works on the classification of protein structures exist in the literature. The main 49 intuition behind these works draws upon a heuristic that generates a signature for each 50 protein strand so that structurally close proteins have similar signatures. Essentially, the 51 signature alignment quantifies the similarity between two protein structures. The problem, 52 however, remains with the speed of computing these signatures and the degree of their 53 representative power. We want a fingerprint for the protein that can be computed fast and 54 can tell whether two proteins are dissimilar or even marginally similar. 55 Some works use vector of frequencies to describe structural features while others take vari- 56 ous physical properties into account such as energy, surface area, volume, flexibility/rigidity 57 or use other features from geometric modeling. The "Bag-Of-Word" (BOW) representation 58 to describe an object has been used in computer vision, natural language processing and 59 various other fields. The work by Budowski-Tal [3] have described protein structure using a 60 fragment library in a similar context. Since we use this work for comparison, we shall discuss 61 its details later. 62 Topological data analysis [10], a newly developed data analysis technique has been 63 shown to give some encouraging results in protein structure analysis. Topological signatures, 64 particularly based on Persistent Homology, enjoy some nice theoretical properties including 65 their robustness and scale invariance. These features are global and more resilient to local 66 perturbations. Moreover, they are invariant to scaling and any isometric transformation of 67 the input. The authors in [23] extract topological fingerprints based on the alignment of 68 atoms and molecules in three dimensional space. Their work shows the impact of persistent 69 homology in the modeling of protein flexibility which is ultimately used in protein B-factor 70 analysis. This work also characterizes the evolution of topology during protein folding and 71 thereby predicts its stability. For this task, the authors have introduced a coarse grain (CG) 72 representation of proteins by considering an amino acid molecule as an atom Cα. This helps 73 them describe the higher level protein structures using the topological fingerprint perfectly. 74 However, since the CG homology may be inconsistent due to ambiguity in choosing the CG T. K. Dey and S. Mandal 6:3 2 Figure 3 Weighted Alpha complex Figure 2 Persistence of a point cloud in R and its corres- ponding barcode for protein structure 75 particle, we present a similar study on secondary structures using our signature and show that 76 our method does not require such a representation as it is inherently scaling independent. 77 The authors in [4] have used persistent homology to generate feature vector in the context 78 of machine learning algorithms applied to protein structure explorations. We explore further 79 to improve upon the technique to eliminate its deficiencies. First, the approach in [4] does not 80 differentiate between atoms belonging to different elements. Also, it does not account for the 81 existing chemical bonds between the atoms while building the signature. Most importantly 82 it uses Vietoris Rips(VR) complex to generate the topological features for protein complex 83 which suffers from the well-known problem of scalability. As we will describe later, the VR 84 complex developed in the early 20th century grows rapidly in size even for moderate size 85 protein structures. Current state-of-the-art techniques, which have addressed the problem to 86 some extent, are still very cumbersome and slow especially for structures having about 30,000 87 atoms on an average. Among the several methods that generate persistence signature from a 88 point cloud, the PHAT toolbox [1] based on several efficient matrix reduction strategies and 89 GUDHI [22] library based on some compression techniques have been popular because of 90 their space and time efficiencies. A recent software called SimBa [8] published last year, has 91 been shown to work faster for large datasets. Yet, for our application, SimBa falls short as 92 we shall see later. 93 The algorithm that we present here is a fast technique to generate a topological signature 3 94 for protein structures. We build our signature based on the coordinates of the atoms in R 95 using their radius as weights. Since we also consider existing chemical bonds between the 96 atoms while building the signature, we believe that the hierarchical convoluted structure of 97 protein is captured in our features. Finally, we have developed a new technique to generate 98 persistence that is much quicker and uses less space than even the current state-of-the-art 99 such as SimBa. It helps us generate the signature even for reasonably large protein structures. 100 In sum, in this paper, we focus on three problems: (1) effectively map a protein structure into 101 a suitable complex; (2) develop a technique to generate fast persistent signature from this 102 complex; (3) use this signature to train a machine learning model for classification and compare 103 against other techniques. Our entire method is summarized in figure 1. We also illustrate 104 this method using a supplementary video available at https://youtu.be/yfcf9UWgdTo. 105 2 Methods 106 We use the theory of topological persistence to generate features for protein structures. These 107 topological features serve as a distinct signature for each protein strand. In this section, we 108 give some background on persistent homology followed by how we construct our signature. WA B I 2 0 1 8 6:4 Protein Classification with Improved Topological Data Analysis 109 2.1 Persistence signature of point cloud data 110 We start with a point cloud data in any n-dimensional Euclidean space. These will essentially 111 be the centers of protein atoms in the three dimensional space. However, to illustrate the 112 theory of persistent homology, we consider a toy example of taking a set of points in two 113 dimensions sampled uniformly from a two-hole structure (Fig.